# Can you solve this collisions problem?

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So, you've got a central elastic collision between two balls. The two balls have opposite momentums. Prove that the kinetic energy of ball 1 before the collision is the same as the kinetic energy of ball 1 after the collision.

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#2

Elastic collision means the energy of the system is conserved. So, the net energy before and after the collision is the same. You mentioned that the objects have opposite momenta. I assume that this means the momenta are equal (Please get back to me ASAP if it's not... I may be missing something here )

Therefore,

Initial momentum = Final momentum

m1u1 + m2u2 = m1v1 + m2v2

But, both momenta are equal.

=> m1u1 = m2u2

Thus, m1u1 = m1v1

As far as I know, this should be right. However, do not hesitate to offer any suggestions, changes, corrections, etc.

~Ri

Therefore,

Initial momentum = Final momentum

m1u1 + m2u2 = m1v1 + m2v2

But, both momenta are equal.

=> m1u1 = m2u2

Thus, m1u1 = m1v1

As far as I know, this should be right. However, do not hesitate to offer any suggestions, changes, corrections, etc.

~Ri

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There's a problem with your solution. Momentum is a vector quantity and in your equation you didn't use the direction of the vectors. The correct equation should be m1u1 - m2u2= -m1v1 + m2v2. Which doesn't really lead somewhere.

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#4

(Original post by

There's a problem with your solution. Momentum is a vector quantity and in your equation you didn't use the direction of the vectors. The correct equation should be m1u1 - m2u2= -m1v1 + m2v2. Which doesn't really lead somewhere.

**Stef_11**)There's a problem with your solution. Momentum is a vector quantity and in your equation you didn't use the direction of the vectors. The correct equation should be m1u1 - m2u2= -m1v1 + m2v2. Which doesn't really lead somewhere.

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#5

(Original post by

So, you've got a central elastic collision between two balls. The two balls have opposite momentums. Prove that the kinetic energy of ball 1 before the collision is the same as the kinetic energy of ball 1 after the collision.

**Stef_11**)So, you've got a central elastic collision between two balls. The two balls have opposite momentums. Prove that the kinetic energy of ball 1 before the collision is the same as the kinetic energy of ball 1 after the collision.

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Guys, no data is given about the mass of the balls. I already mentioned that the collsion is head-on ( I said it is a CENTRAL collision) . This problem is an actual problem from a physics book, which doesn't include the answer. I didn't make up the problem. Your guess about the balls is as good as mine.

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#7

(Original post by

Guys, no data is given about the mass of the balls. I already mentioned that the collsion is head-on ( I said it is a CENTRAL collision) . This problem is an actual problem from a physics book, which doesn't include the answer. I didn't make up the problem. Your guess about the balls is as good as mine.

**Stef_11**)Guys, no data is given about the mass of the balls. I already mentioned that the collsion is head-on ( I said it is a CENTRAL collision) . This problem is an actual problem from a physics book, which doesn't include the answer. I didn't make up the problem. Your guess about the balls is as good as mine.

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If the balls are of equal mass, I need to prove it. If they don't, I still need to prove that V1=v1' and yes, I did use mainly algebraic manipulation when I attempted to prove the latter, however, with no result. Basically, I was only getting relationships that I already knew to be true.

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#9

(Original post by

If the balls are of equal mass, I need to prove it. If they don't, I still need to prove that V1=v1' and yes, I did use mainly algebraic manipulation when I attempted to prove the latter, however, with no result. Basically, I was only getting relationships that I already knew to be true.

**Stef_11**)If the balls are of equal mass, I need to prove it. If they don't, I still need to prove that V1=v1' and yes, I did use mainly algebraic manipulation when I attempted to prove the latter, however, with no result. Basically, I was only getting relationships that I already knew to be true.

_{1}=v

_{1}if that's what you mean but, thinking about it again, I don't think we could prove this mathematically. The idea of K.E being conserved in an elastic collision is assumed to be true on the basis of the concept of conservation of energy.

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But KE being conserved applies only for the KE of the system before an after the collision, not for individual KEs.

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#11

(Original post by

But KE being conserved applies only for the KE of the system before an after the collision, not for individual KEs.

**Stef_11**)But KE being conserved applies only for the KE of the system before an after the collision, not for individual KEs.

*must*travel back

*with the same velocity*in opposite direction to their original velocity.

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#12

**Stef_11**)

There's a problem with your solution. Momentum is a vector quantity and in your equation you didn't use the direction of the vectors. The correct equation should be m1u1 - m2u2= -m1v1 + m2v2. Which doesn't really lead somewhere.

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#14

(Original post by

We don't know the bodies are of equal mass. 😔

**Stef_11**)We don't know the bodies are of equal mass. 😔

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#15

His other thread is here:

http://www.thestudentroom.co.uk/show....php?t=3736243

You should quote someone if you want a reply. I just saw this thread and checked your other one.

I think you're confused on conservation of momentum. If the initial momentums are equal and opposite, what is the total initial momentum?

http://www.thestudentroom.co.uk/show....php?t=3736243

(Original post by

I mentioned that the momentums of the balls are opposite i.e they have the same magnitude and opposite directions. I didn't mention that the momentums are opposite INITIALLY, my bad. Anyway, in all my efforts I have made use of the following relationships:

**Stef_11**)I mentioned that the momentums of the balls are opposite i.e they have the same magnitude and opposite directions. I didn't mention that the momentums are opposite INITIALLY, my bad. Anyway, in all my efforts I have made use of the following relationships:

**m1v1 - m2v2= -m1v1' + m2v2'**and KE1 + KE2=KE1' + KE2'. I also used p1=p2 and p1'=p2'. My goal is basically to prove that V1=v1'. I used the above relationships in many different ways, solving and substituting but that doesn't lead me anywhere, only to relationships I know to be true. Any ideas?I think you're confused on conservation of momentum. If the initial momentums are equal and opposite, what is the total initial momentum?

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#16

(Original post by

His other thread is here:

http://www.thestudentroom.co.uk/show....php?t=3736243

You should quote someone if you want a reply. I just saw this thread and checked your other one.

I think you're confused on conservation of momentum. If the initial momentums are equal and opposite, what is the total initial momentum?

**morgan8002**)His other thread is here:

http://www.thestudentroom.co.uk/show....php?t=3736243

You should quote someone if you want a reply. I just saw this thread and checked your other one.

I think you're confused on conservation of momentum. If the initial momentums are equal and opposite, what is the total initial momentum?

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#17

(Original post by

I think he's taken away the initial momentum to take the direction of velocities into account. How would you go about proving the conservation of K.E by considering the total initial momentum to be zero?

**Mehrdad jafari**)I think he's taken away the initial momentum to take the direction of velocities into account. How would you go about proving the conservation of K.E by considering the total initial momentum to be zero?

There are three pieces of information: conservation of kinetic energy, conservation of momentum, equal and opposite initial momentum. I did it by writing the last two of these in equation form, combining them and substituting into the first.

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#18

(Original post by

Conservation of kinetic energy is given in the question(elastic).

There are three pieces of information: conservation of kinetic energy, conservation of momentum, equal and opposite initial momentum. I did it by writing the last two of these in equation form, combining them and substituting into the first.

**morgan8002**)Conservation of kinetic energy is given in the question(elastic).

There are three pieces of information: conservation of kinetic energy, conservation of momentum, equal and opposite initial momentum. I did it by writing the last two of these in equation form, combining them and substituting into the first.

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#19

(Original post by

True, elastic is a key word here but I couldn't show it mathematically. Although I did find the kinetic energy of the system initially in terms of the final kinetic energy, I couldn't see how they were equal.

**Mehrdad jafari**)True, elastic is a key word here but I couldn't show it mathematically. Although I did find the kinetic energy of the system initially in terms of the final kinetic energy, I couldn't see how they were equal.

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